Pi still seems to be open for new players, so you should be able to invite new players.
First, ensure that you've completed the tutorial. Then look on the map for one of the empty slots on an island. Click on it, and it should bring up the 'Invite friends' window. From there, click on 'via link', select the link that you are given, and give that link to a friend. That link will then let your friend start an account on Pi with a city in that slot.
One thing to note is that you can not invite someone to a world, if they already have a registered account. If your friend already has an account on other worlds, they will either need to start on this world in a random location and hope to be close to you, or will have to register a new account in order to use your link.
